a parallelogram has an area of 150 cm^2. the side lengths are 80 cm and 40 cm what are the measures of the angles

To find the measures of the angles in a parallelogram, we can use the fact that opposite angles in a parallelogram are equal.

Step 1: Calculate the base and height of the parallelogram.
Since the area of the parallelogram is given as 150 cm^2, we can use the formula for the area of a parallelogram: area = base × height. In this case, the area is 150 cm^2, and one of the side lengths is 80 cm.

Let's assume that the side lengths 80 cm and 40 cm correspond to the base and height, respectively, or vice versa.

If we assume the length of 80 cm as the base, we can calculate the height:
area = base × height
150 cm^2 = 80 cm × height
height = 150 cm^2 / 80 cm
height = 1.875 cm

So, the base of the parallelogram is 80 cm, and the corresponding height is 1.875 cm.

If we assume the length of 40 cm as the base, we can calculate the height:
area = base × height
150 cm^2 = 40 cm × height
height = 150 cm^2 / 40 cm
height = 3.75 cm

So, the base of the parallelogram is 40 cm, and the corresponding height is 3.75 cm.

Step 2: Calculate the angles of the parallelogram.
Since opposite angles in a parallelogram are equal, we can use the fact that the opposite sides in a parallelogram are equal in length.

Let's label the angles of the parallelogram as A, B, C, and D.

Angle A is opposite angle C, and angle B is opposite angle D.

Using the given side lengths, we know that sides AB and CD have lengths of 80 cm, and sides BC and DA have lengths of 40 cm.

Since AB and CD are equal in length, angle A is equal to angle C.

Since BC and DA are equal in length, angle B is equal to angle D.

Therefore, angles A and C are equal, as are angles B and D.

So, to find the measures of the angles, we need to determine angle A or angle C (as they are equal) and angle B or angle D (as they are equal).

To find angle A (or C), we can use the following formula:
angle A (or C) = arctan(height / base)

If we assume the length of 80 cm as the base, we get:
angle A = arctan(1.875 / 80) ≈ 1.39 degrees

If we assume the length of 40 cm as the base, we get:
angle A = arctan(3.75 / 40) ≈ 5.71 degrees

So, depending on which side we assume as the base, angle A (or C) is approximately 1.39 degrees or 5.71 degrees.

Since angles A and C are equal, the measures of angles A and C are both approximately 1.39 degrees or 5.71 degrees.

Similarly, angles B and D are also equal, with the same measures.

Therefore, the measures of the angles in the parallelogram are approximately:
Angle A = Angle C ≈ 1.39 degrees or 5.71 degrees
Angle B = Angle D ≈ 1.39 degrees or 5.71 degrees